CS 154
Intro. to Automata and Complexity Theory
Handout 6
Autumn 2006
David Dill
October 10, 2006
Problem Set 2
Due: October 17, 2006
Homework:
(Total 100 points + 20 extra) Do the following exercises.
Problem 1.
[10 points]
Consider the
NFA defined in the following tran
sition table.
a
b
c
→
p
{
q, r
}
{
q
}
{
r
}
∅
q
{
p, q
}
∅
{
p
}
{
p, r
}
*
r
∅
∅
∅
∅
a).
Compute the
closure of each state.
b).
Convert this
NFA into an DFA using the construction described in
class. You must provide the transition table of the resulting DFA.
Problem 2.
[20 points]
Provide regular expressions for the following lan
guages over the alphabet Σ =
{
0
,
1
}
. Provide a brief explanation as to why
your regular expressions generate the given languages.
a).
The set of all strings not containing 111 as a substring.
b).
The set of all strings in which all pairs of adjacent 0’s appears before
all pairs of adjacent 1’s.
Problem 3.
[15 points]
Consider the DFA
M
= (
Q,
Σ
, δ, q
0
, F
) with
Q
=
{
1
,
2
,
3
,
4
}
, Σ =
{
a, b, c
}
,
q
0
= 1,
F
=
{
4
}
, and
δ
as defined in the following
transition diagram.
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 Winter '08
 Motwani,R
 Formal language, Regular expression, Regular language, Automata theory

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